A Ph.D. is a much longer endeavor than I had originally thought, and I have many people to thank for getting me through it. This list is far from exhaustive, but I would like to single out people who played particularly strong roles during my extended stay at SEP.

I would like to start by thanking my senior students and mentors Morgan Brown, Bob Clapp, and Antoine Guitton. They led me toward a research project and pro- vided many hours of conversation about it and many other topics of mutual interest in geophysics and computing. I have since had the pleasure of having Bob on my de- fense committee and Antoine as a supervisor during an internship, and learned even more from them as a result. I thank my cohort, Gabriel Alvarez, Brad Artman, An- drey Karpushin, and Nick Vlad, who I shared many experiences with, and who gave me much needed support. I also thank the many students who arrived before and after me, in particular Guojian Shan, Jesse Lomask, Daniel Rosales, Doug Gratwick, Alejandro Valenciano, Jeff Shragge, Yaxun Tang, Madhav Vyas, Pierre Jousselin, Ben Witten, Claudio Cardoso, Gboyega Ayeni, and Roland Gunther for many useful discussions about our research and the world at large.

I owe a large debt to Jon Claerbout and Biondo Biondi for establishing and main- taining the intellectual framework of SEP and for keeping us focused on interesting topics that have applicability in the real world. They have given me the viewpoint that research is the most fun when working on new ways to approach a difficult field data set. Diane Lau deserves much credit for keeping a group as large as SEP running smoothly, and I owe the sponsors of SEP much for their financial support.
Anyone reading this thesis should thank Ken Larner for taking what was a semi- intelligible mess and helping me rewrite and refine it into what you are reading today. He was extremely supportive and helpful during his brief stay at SEP. Norm Sleep also deserves much credit for his thorough review of this thesis. It is much stronger because of his help.

Doug Schmitt and Mauricio Sacchi at the University of Alberta sparked my in- terest in geophysics, and I enjoyed their courses greatly. Bill MacDonald was my supervisor during an extended internship in Calgary. He sent me out on a seismic survey for a week, which got me thinking about interpolation as a research topic.

I would like to thank my many friends at Stanford and elsewhere who helped me in my attempt to remain as well-rounded as possible. They are too numerous to mention, and are in geophysics, earth sciences, and further abroad.

Finally, I thank my family: my father and my brother for their focus on science and education, and my mother for her continual support.